## Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration |

Optics Express, Vol. 20, Issue 27, pp. 29063-29075 (2012)

http://dx.doi.org/10.1364/OE.20.029063

Acrobat PDF (4688 KB)

### Abstract

We present a new instrumentation and calibration procedure for terahertz time-domain spectroscopic ellipsometry (THz-TDSE) that is a newly established characterization technique. The experimental setup is capable of providing arbitrary angle of incidence in the range of 15°–85° in the reflection geometry, and with no need for realignment. The setup is also configurable easily into transmission geometry. For this setup, we successfully used hollow core photonic band gap fiber with no pre-chirping in order to deliver a femtosecond laser into a THz photoconductive antenna detector, which is the first demonstration of this kind. The proposed calibration scheme can compensate for the non-ideality of the polarization response of the THz photoconductive antenna detector as well as that of wire grid polarizers used in the setup. In the calibration scheme, the ellipsometric parameters are obtained through a regression algorithm which we have adapted from the conventional regression calibration method developed for rotating element optical ellipsometers, and used here for the first time for THz-TDSE. As a proof-of-principle demonstration, results are presented for a high resistivity silicon substrate as well as an opaque Si substrate with a high phosphorus concentration. We also demonstrate the capacity to measure a few micron thick grown thermal oxide on top of Si. Each sample was characterized by THz-TDSE in reflection geometry with different angle of incidence.

© 2012 OSA

## 1. Introduction

1. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B **7**, 2006–2015 (1990). [CrossRef]

4. L. Bilbro, R. V. Aguilar, G. Logvenov, O. Pelleg, I. Bozovic, and N. P. Armitage, “Temporal correlations of superconductivity above the transition temperature in La_{2−x}Sr* _{x}*CuO

_{4}probed by terahertz spectroscopy,” Nat. Phys.

**7**, 298 (2011). [CrossRef]

5. S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. **79**, 3923 (2001). [CrossRef]

6. A. Pashkin, M. Kempa, H. Nemec, F. Kadlec, and P. Kuzel, “Phase-sensitive time-domain terahertz reflection spectroscopy,” Rev. Sci. Instrum. **74**, 4711 (2003). [CrossRef]

_{3}bulk single crystals and the dielectric constants of doped GaAs thin films [14

14. T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. **79**, 3917–3919 (2001). [CrossRef]

16. N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett. **36**, 265–267 (2011). [CrossRef] [PubMed]

17. A. Rubano, L. Braun, M. Wolf, and T. Kampfrath, “Mid-infrared time-domain ellipsometry: Application to Nb-doped SrTiO_{3},” Appl. Phys. Lett. **101**, 081103 (2012). [CrossRef]

18. R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, “Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs,” Appl. Phys. Lett. **81**, 199–201 (2002). [CrossRef]

26. N. Yasumatsu and S. Watanabe, “T-ray topography by time-domain polarimetry,” Opt. Lett. **37**, 2706–2708 (2012). [CrossRef] [PubMed]

## 2. Instrumentation

*θ*< 85°) in reflection mode, and can be easily configurable in transmission mode by aligning the arms along a straight line (Fig. 1(c)).

*f*confocal geometry with terahertz lenses made of poly-4-methyl-pentacene-1 (TPX), which is a terahertz- and optically transparent material. Terahertz lenses have 50.8 mm clear aperture diameter and 100 mm focal length, and are less prone to misalignments and polarization distortion as compared to off-axis parabolic mirrors. The terahertz beam profile can be approximated as Gaussian. The sample is placed at the focal point of the terahertz lenses where an effective flat phase front exist at the beam waist. Based on the Gaussian beam assumption and 100 mm focal length for the THz lenses, the

*f*# is approximately 9 for 0.2 THz. In the present case, the strong focusing and long wavelengths minimize the effects of a spread of incidence angles because an effective flat phase front exists at the sample position. This is the opposite approach than has been used in previous infrared ellipsometers that were designed to work at high

*f*# [13

13. J. Kircher, R. Henn, M. Cardona, P. L. Richards, and G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B **14**, 705–712 (1997). [CrossRef]

*μ*m and 25

*μ*m, respectively, and field extinction ratio of ∼ 40 : 1 at 1 THz.

*μ*m, and the mode-field diameter is 5.5

*μ*m. Attenuation through the low-loss region is reported as < 250 dB/km. The fiber is connected from one side to a fiber launcher with a focusing lens and a 3-axis positioner, and from the other side is connected to a fiber-coupled focusing optics that is attached to the THz detector compartment.

## 3. Formulation

**E**

*= [*

_{i}*E*

_{ip}*E*] with close to linear polarization state and azimuthal angle around 45°. After passing through the polarizer, the polarization state becomes highly linear at the azimuthal angle of the polarizer

_{is}*ϕ*. The reflected polarization state is then modified according to the ellipsometric parameters (Ψ, Δ) of the sample. The

_{p}*p*- and

*s*-component of the reflected polarization state are detected by setting the azimuthal angle of the analyzer at

*ϕ*= 0° and 90°, respectively.

_{a}**E**

*= [*

_{r}*E*

_{rp}*E*] as shown in Fig. 4, is determined by the product of the Jones matrices of the polarizer

_{rs}**J**

*, sample*

_{P}**J**

*, and analyzer*

_{S}**J**

*as [7] where*

_{A}**R**(

*ϕ*) is the rotation matrix with angle

*ϕ*. The Jones matrices for the sample and the polarizer/analyzer are given as [7] where

*η*

_{P(A)}is the extinction ratio of the polarizer(analyzer), defined as the ratio of the transmitted electric field when the polarizer transmission axis is perpendicular and parallel to the electric field direction, and

*δ*

_{P(A)}is the phase retardance. For an ideal polarizer/analyzer the extinction ratio is zero (

*η*

_{P(A)}= 0).

19. E. Castro-Camus, J. Lloyd-Hughes, L. Fu, H.H. Tan, C. Jagadish, and M. B. Johnston, “An ion-implanted InP receiver for polarization resolved terahertz spectroscopy,” Opt. Express **15**, 7047–7057 (2007). [CrossRef] [PubMed]

**P**

*= [*

_{d}*P*

_{p}*P*], which is generally frequency dependent. In the frequency domain, the spectrum of the output signal of the photoconductive antenna detector can be expressed by an inner product as [30

_{s}30. M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett. **37**, 1811–1813 (2012). [CrossRef] [PubMed]

*I*is the Fourier transform (spectrum) of the THz detector output signal,

**E**

*is the electric field vector impinging on the detector as shown in Fig. 4, and*

_{r}*ω*is the angular frequency. We define a complex parameter

*ρ*as the ratio of the detector output spectrum when the transmission axis of the analyzer is along

*p*- and

*s*-axis which corresponds to

*ϕ*= 0° and 90°, respectively, as where

_{a}*I*

_{mod}and

*I*

_{exp}refer to the detector output spectrum calculated through the model described by Eqs. (2)–(4), and obtained directly from the experiment, respectively. From Eqs. (2)–(4), it is clear that the

*ρ*-parameter is a function of the sample ellipsometric parameters (Ψ, Δ), azimuthal angle of the polarizer

*ϕ*, and the extinction ratio and phase retardance of both polarizer and analyzer. It is worth noting that under ideal conditions, i.e.

_{p}*η*

_{P(A)}= 0 and

*ϕ*= 45°, the ellipsometric parameters of the sample can be directly extracted from the

_{p}*ρ*-parameter as where

*arg*(.) denotes the phase operator.

## 4. Measurement and calibration procedure

**P**

*, extinction ratio and phase retardance of the polarizer/analyzer as well as their azimuthal offset angles Δ*

_{d}*ϕ*/Δ

_{p}*ϕ*with respect to the

_{a}*p*-axis. Azimuthal offset angles may arise due to the uncertainty in the polarizer (analyzer), or the misalignment of the components (e.g. surface tilt of the sample), and can be easily modeled by replacing

**R**(

*ϕ*

_{p(a)}) with

**R**(

*ϕ*

_{p(a)}+ Δ

*ϕ*

_{p(a)}) in Eq. (2).

**P**

*can be obtained experimentally over the desired frequency range through a calibration scheme reported elsewhere [30*

_{d}30. M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett. **37**, 1811–1813 (2012). [CrossRef] [PubMed]

30. M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett. **37**, 1811–1813 (2012). [CrossRef] [PubMed]

**P**

*is known from Eq. (7) and through the reflection measurement from a gold mirror, the ellipsometric parameters are obtained through a regression algorithm which we have adapted from the conventional regression calibration method developed by B. Johs for rotating element optical ellipsometers [31*

_{d}31. B. Johs, “Regression calibration method for rotating element ellipsometers,” Thin Solid Films **234**, 395 – 398 (1993). [CrossRef]

*ρ*-parameter defined in Eq. 5 is obtained experimentally (

*ρ*

_{exp}) from an isotropic sample at one or several different azimuthal angles of the polarizer (

*ϕ*,

_{pi}*i*= 1,…,

*N*). Then, the

*ρ*-parameter from the model (

*ρ*

_{mod}) described by Eqs. (2)–(5) is fitted to that from the experiment over the desired frequency range and simultaneously for all the polarizer azimuthal angles, using the Levenberg-Marquardt nonlinear regression algorithm. We define an error function

*Err*based on least squares fitting as

*η*

_{P(A)},

*δ*

_{P(A)}and Δ

*ϕ*

_{p(a)}are simultaneously found such that the error function defined in Eq. (11) is minimized over the measurement frequency range (

*ω*,

_{j}*j*= 1,…,

*M*) and for all measured data sets corresponding to different polarizer angles (

*ϕ*,

_{pi}*i*= 1,…,

*N*). The advantage of this technique is that the polarizer/analyzer parameters do not need to be a priori knowledge, although reasonable initial values are necessary for the convergence of the regression algorithm. It was found that the best initial values for Ψ and Δ are those obtained from Eq. (6) when

*ρ*=

*ρ*

_{exp}.

## 5. Experimental results and discussion

*ρ*-parameter to three sets of measured data corresponding to polarizer angles

*ϕ*

_{p1}= 25°,

*ϕ*

_{p2}= 45° and

*ϕ*

_{p3}= 65°. The uncalibrated plot is directly obtained from Eq. (6) using the data set corresponding to

*ϕ*

_{p2}= 45°. An incidence angle of 45° (away from the Brewster’s angle) was used for this experiment so as to have appreciable signal in both the

*s*– and

*p*– polarizations.

1. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B **7**, 2006–2015 (1990). [CrossRef]

*ρ*

_{mod}to

*ρ*

_{exp}for the highly doped silicon sample over the frequency range 0.1–1.5 THz. The fitting was performed simultaneously for three sets of data corresponding to three different azimuthal angle of the polarizer. Ellipsometric parameters Ψ and Δ along with polarizer/analyzer extinction ratios, phase retardances and offset angles were the free parameters of the regression algorithm in this least squares fitting. This highly doped silicon sample is opaque in the THz range and cannot be measured in transmission. The incidence angle was 73°, which is close to the Brewster angle of silicon.

*ρ*= 0.011 Ω-cm and

*τ*= 190 fs from the fitting and by assuming an effective electron mass of 0.26

*m*

_{0}[32

32. M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. **56**, 1694–1696 (1990). [CrossRef]

8. T. Hofmann, C. M. Herzinger, A. Boosalis, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Variable-wavelength frequency-domain terahertz ellipsometry,” Rev. Sci. Instrum. **81**, 023101 (2010). [CrossRef] [PubMed]

*μ*m using optical techniques. Figure 9 compares the measured ellipsometric parameters of the highly doped Si substrate before and after oxidization. The thickness of the oxide thin-film was extracted by fitting a thin-film/substrate model to the measured ellipsometric parameters. We used the same refractive index in Fig. 8(a) for the substrate, and considered the refractive index of the thin-film as well as its thickness as free parameters in the fitting process. The resultant thickness of the oxide thin-film was obtained as 1.9

*μ*m that is in excellent agreement with that obtained from the independent method. The fact that we can measure dielectric thicknesses that are only 0.3% of the free space wavelength of 500 GHz radiation further shows the high accuracy of the technique. In order to avoid water vapor absorption, the space with terahertz wave propagation was enclosed and purged with dry air during the above measurements.

## 6. Conclusion

## Acknowledgments

## References and links

1. | D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B |

2. | B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol. |

3. | D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B: Lasers Opt. |

4. | L. Bilbro, R. V. Aguilar, G. Logvenov, O. Pelleg, I. Bozovic, and N. P. Armitage, “Temporal correlations of superconductivity above the transition temperature in La _{4} probed by terahertz spectroscopy,” Nat. Phys. 7, 298 (2011). [CrossRef] |

5. | S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett. |

6. | A. Pashkin, M. Kempa, H. Nemec, F. Kadlec, and P. Kuzel, “Phase-sensitive time-domain terahertz reflection spectroscopy,” Rev. Sci. Instrum. |

7. | H. Fujiwara, |

8. | T. Hofmann, C. M. Herzinger, A. Boosalis, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Variable-wavelength frequency-domain terahertz ellipsometry,” Rev. Sci. Instrum. |

9. | A. Röseler, |

10. | K.-L. Barth, D. Bhme, K. Kamars, F. Keilmann, and M. Cardona, “Far-ir spectroscopic ellipsometer,” Thin Solid Films |

11. | J. Bremer, O. Hunderi, K. Fanping, T. Skauli, and E. Wold, “Infrared ellipsometer for the study of surfaces, thin films, and superlattices,” Appl. Opt. |

12. | C. Bernhard, J. Humlcek, and B. Keimer, “Far-infrared ellipsometry using a synchrotron light source–the dielectric response of the cuprate high Tc superconductors,” Thin Solid Films |

13. | J. Kircher, R. Henn, M. Cardona, P. L. Richards, and G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B |

14. | T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett. |

15. | N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, “Measurement of the soft-mode dispersion in SrTiO |

16. | N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett. |

17. | A. Rubano, L. Braun, M. Wolf, and T. Kampfrath, “Mid-infrared time-domain ellipsometry: Application to Nb-doped SrTiO |

18. | R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, “Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs,” Appl. Phys. Lett. |

19. | E. Castro-Camus, J. Lloyd-Hughes, L. Fu, H.H. Tan, C. Jagadish, and M. B. Johnston, “An ion-implanted InP receiver for polarization resolved terahertz spectroscopy,” Opt. Express |

20. | H. Dong, Y. Gong, V. Paulose, and M. Hong, “Polarization state and mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun. |

21. | J. L. M. van Mechelen, D. van der Marel, I. Crassee, and T. Kolodiazhnyi, “Spin resonance in eutio |

22. | J. N. Hancock, J. L. M. van Mechelen, A. B. Kuzmenko, D. van der Marel, C. Brüne, E. G. Novik, G. V. Astakhov, H. Buhmann, and L. W. Molenkamp, “Surface state charge dynamics of a high-mobility three-dimensional topological insulator,” Phys. Rev. Lett. |

23. | R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Černe, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal kerr rotation from the surface states of the topological insulator Bi |

24. | C. M. Morris, R. V. Aguilar, A. V. Stier, and N. P. Armitage, “Polarization modulation time-domain terahertz polarimetry,” Opt. Express |

25. | D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Černe, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B |

26. | N. Yasumatsu and S. Watanabe, “T-ray topography by time-domain polarimetry,” Opt. Lett. |

27. | C. J. Hensley, M. A. Foster, B. Shim, and A. L. Gaeta, “Extremely high coupling and transmission of high-powered-femtosecond pulses in hollow-core photonic band-gap fiber,” in “ |

28. | M. Born and E. Wolf, |

29. | Y. Gong, H. Dong, and Z. Chen, “Cross-polarization response of a two-contact photoconductive terahertz detector,” Terahertz Sci. Technol. |

30. | M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett. |

31. | B. Johs, “Regression calibration method for rotating element ellipsometers,” Thin Solid Films |

32. | M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett. |

**OCIS Codes**

(120.3940) Instrumentation, measurement, and metrology : Metrology

(120.5410) Instrumentation, measurement, and metrology : Polarimetry

(040.2235) Detectors : Far infrared or terahertz

**ToC Category:**

Instrumentation, Measurement, and Metrology

**History**

Original Manuscript: September 4, 2012

Revised Manuscript: November 26, 2012

Manuscript Accepted: November 26, 2012

Published: December 14, 2012

**Citation**

Mohammad Neshat and N. P. Armitage, "Terahertz time-domain spectroscopic ellipsometry: instrumentation and calibration," Opt. Express **20**, 29063-29075 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-27-29063

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### References

- D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with terahertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B7, 2006–2015 (1990). [CrossRef]
- B. M. Fischer, M. Walther, and P. U. Jepsen, “Far-infrared vibrational modes of DNA components studied by terahertz time-domain spectroscopy,” Phys. Med. Biol.47, 3807 (2002). [CrossRef] [PubMed]
- D. Mittleman, R. Jacobsen, R. Neelamani, R. Baraniuk, and M. Nuss, “Gas sensing using terahertz time-domain spectroscopy,” Appl. Phys. B: Lasers Opt.67, 379–390 (1998). [CrossRef]
- L. Bilbro, R. V. Aguilar, G. Logvenov, O. Pelleg, I. Bozovic, and N. P. Armitage, “Temporal correlations of superconductivity above the transition temperature in La2−xSrxCuO4 probed by terahertz spectroscopy,” Nat. Phys.7, 298 (2011). [CrossRef]
- S. Nashima, O. Morikawa, K. Takata, and M. Hangyo, “Measurement of optical properties of highly doped silicon by terahertz time domain reflection spectroscopy,” Appl. Phys. Lett.79, 3923 (2001). [CrossRef]
- A. Pashkin, M. Kempa, H. Nemec, F. Kadlec, and P. Kuzel, “Phase-sensitive time-domain terahertz reflection spectroscopy,” Rev. Sci. Instrum.74, 4711 (2003). [CrossRef]
- H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).
- T. Hofmann, C. M. Herzinger, A. Boosalis, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Variable-wavelength frequency-domain terahertz ellipsometry,” Rev. Sci. Instrum.81, 023101 (2010). [CrossRef] [PubMed]
- A. Röseler, Infrared Spectroscopic Ellipsometry (Akademie-Verlag, 1990).
- K.-L. Barth, D. Bhme, K. Kamars, F. Keilmann, and M. Cardona, “Far-ir spectroscopic ellipsometer,” Thin Solid Films234, 314 – 317 (1993). [CrossRef]
- J. Bremer, O. Hunderi, K. Fanping, T. Skauli, and E. Wold, “Infrared ellipsometer for the study of surfaces, thin films, and superlattices,” Appl. Opt.31, 471–478 (1992). [CrossRef] [PubMed]
- C. Bernhard, J. Humlcek, and B. Keimer, “Far-infrared ellipsometry using a synchrotron light source–the dielectric response of the cuprate high Tc superconductors,” Thin Solid Films455, 143 –149 (2004).
- J. Kircher, R. Henn, M. Cardona, P. L. Richards, and G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B14, 705–712 (1997). [CrossRef]
- T. Nagashima and M. Hangyo, “Measurement of complex optical constants of a highly doped Si wafer using terahertz ellipsometry,” Appl. Phys. Lett.79, 3917–3919 (2001). [CrossRef]
- N. Matsumoto, T. Fujii, K. Kageyama, H. Takagi, T. Nagashima, and M. Hangyo, “Measurement of the soft-mode dispersion in SrTiO3 by terahertz time-domain spectroscopic ellipsometry,” Jpn. J. Appl. Phys.48, 09KC11 (2009). [CrossRef]
- N. Matsumoto, T. Hosokura, T. Nagashima, and M. Hangyo, “Measurement of the dielectric constant of thin films by terahertz time-domain spectroscopic ellipsometry,” Opt. Lett.36, 265–267 (2011). [CrossRef] [PubMed]
- A. Rubano, L. Braun, M. Wolf, and T. Kampfrath, “Mid-infrared time-domain ellipsometry: Application to Nb-doped SrTiO3,” Appl. Phys. Lett.101, 081103 (2012). [CrossRef]
- R. Shimano, Y. Ino, Y. P. Svirko, and M. Kuwata-Gonokami, “Terahertz frequency Hall measurement by magneto-optical Kerr spectroscopy in InAs,” Appl. Phys. Lett.81, 199–201 (2002). [CrossRef]
- E. Castro-Camus, J. Lloyd-Hughes, L. Fu, H.H. Tan, C. Jagadish, and M. B. Johnston, “An ion-implanted InP receiver for polarization resolved terahertz spectroscopy,” Opt. Express15, 7047–7057 (2007). [CrossRef] [PubMed]
- H. Dong, Y. Gong, V. Paulose, and M. Hong, “Polarization state and mueller matrix measurements in terahertz-time domain spectroscopy,” Opt. Commun.282, 3671–3675 (2009). [CrossRef]
- J. L. M. van Mechelen, D. van der Marel, I. Crassee, and T. Kolodiazhnyi, “Spin resonance in eutio3 probed by time-domain gigahertz ellipsometry,” Phys. Rev. Lett.106, 217601 (2011). [CrossRef] [PubMed]
- J. N. Hancock, J. L. M. van Mechelen, A. B. Kuzmenko, D. van der Marel, C. Brüne, E. G. Novik, G. V. Astakhov, H. Buhmann, and L. W. Molenkamp, “Surface state charge dynamics of a high-mobility three-dimensional topological insulator,” Phys. Rev. Lett.107, 136803 (2011). [CrossRef] [PubMed]
- R. V. Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Černe, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett.108, 087403 (2012). [CrossRef]
- C. M. Morris, R. V. Aguilar, A. V. Stier, and N. P. Armitage, “Polarization modulation time-domain terahertz polarimetry,” Opt. Express20, 12303–12317 (2012). [CrossRef] [PubMed]
- D. K. George, A. V. Stier, C. T. Ellis, B. D. McCombe, J. Černe, and A. G. Markelz, “Terahertz magneto-optical polarization modulation spectroscopy,” J. Opt. Soc. Am. B29, 1406 (2012). [CrossRef]
- N. Yasumatsu and S. Watanabe, “T-ray topography by time-domain polarimetry,” Opt. Lett.37, 2706–2708 (2012). [CrossRef] [PubMed]
- C. J. Hensley, M. A. Foster, B. Shim, and A. L. Gaeta, “Extremely high coupling and transmission of high-powered-femtosecond pulses in hollow-core photonic band-gap fiber,” in “Proceedings of Lasers and Electro-Optics,” (San Jose, Calif., 2008), p. JFG1.
- M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), chap. 14.
- Y. Gong, H. Dong, and Z. Chen, “Cross-polarization response of a two-contact photoconductive terahertz detector,” Terahertz Sci. Technol.4, 137–148 (2011).
- M. Neshat and N. P. Armitage, “Improved measurement of polarization state in terahertz polarization spectroscopy,” Opt. Lett.37, 1811–1813 (2012). [CrossRef] [PubMed]
- B. Johs, “Regression calibration method for rotating element ellipsometers,” Thin Solid Films234, 395 – 398 (1993). [CrossRef]
- M. van Exter and D. Grischkowsky, “Optical and electronic properties of doped silicon from 0.1 to 2 THz,” Appl. Phys. Lett.56, 1694–1696 (1990). [CrossRef]

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